It is not proven that Mozart and the young Beethoven ever met. Beethoven was indeed in Vienna in 1787 in the age of 16 to learn music, not in 1790, as in the movie. However they didn't meet as as Mozart took care of his sick father Leopold who died the same year and Beethoven had to leave due to the sickness of his mother. He only came back to Vienna years after Mozart died.
While it is correct that Mozart didn't receive the full 500 guilder for his opera "The Abduction from the Seraglio" but his final gain was 100 guilder and not 426,40 as Mozart said it in the movie.
Beethoven is playing Mozart his Moonlight Sonata in 1790, which it was written in 1801. Furthermore it was not improvised as in the movie but was written for a blind girl who wanted to know how the moon is lighting.
Sophie Weber told Mozart that Aloisia is not in Vienna but stayed in Munich because she married Joseph Lange. However this happened in Vienna where Aloisia later worked as a singer and performed with Mozart.
Strack said that Mozart finally would love to write an opera. However by the time he was in Vienna, which is since 1781, Mozart already wrote 11 operas, being the first written in 1767.
Mozart's dog Pimperl died in 1784 while in the movie he is alive in 1790.
The first scene is set in 1778. However "Ein Mädchen oder Weibchen" from Mozart's "Magic Flute" is played, which was released in 1791, shortly before his death.